Question

The residents of a certain country value boys over girls, and every couple makes sure a boy is born in the family. So, if the first child is a boy, they stop there. If the first child is a girl, they have another child, and keep on having children until the first boy. So, the progression of children for each family ends with a boy. Some examples would be B, GB, GGB, GGGGB. At birth, the probability of a child being a girl or a boy is equal (1/2). (a) What is the expected number of children of a family? (b) What is the expected value of the proportion of males to the total population in this country?

          The residents of a certain country value boys over girls, and every couple makes sure a boy is born in the family. So, if the first child is a boy, they stop there. If the first child is a girl, they have another child, and keep on having children until the first boy. So, the progression of children for each family ends with a boy. Some examples would be B, GB, GGB, GGGGB.

At birth, the probability of a child being a girl or a boy is equal (1/2).

(a) What is the expected number of children of a family?
(b) What is the expected value of the proportion of males to the total population in this country?

The residents of a certain country value boys over girls, and every couple makes sure a boy is born in the family. So, if the first child is a boy, they stop there. If the first child is a girl, they have another child, and keep on having children until the first boy. So, the progression of children for each family ends with a boy. Some examples would be B, GB, GGB, GGGGB.

At birth, the probability of a child being a girl or a boy is equal (1/2).

(a) What is the expected number of children of a family?
(b) What is the expected value of the proportion of males to the total population in this country?

Added by Barbara P.

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